In algebraic geometry, a proper morphism between schemes is an analog of a proper map between complex analytic spaces.
Some authors call a proper variety over a field k a complete variety. For example, every projective variety over a field k is proper over k. A scheme X of finite type over the complex numbers (for example, a variety) is proper over C if and only if the space X(C) of complex points with the classical (Euclidean) topology is compact and Hausdorff.
A closed immersion is proper. A morphism is finite if and only if it is proper and quasi-finite.
X → Y be a morphism of schemes. The composition of two propermorphisms is proper. Any base change of a propermorphism f: X → Y is proper. That is, if...
is called proper if inverse images of compact subsets are compact. In algebraic geometry, the analogous concept is called a propermorphism. There are...
compact subsets are compact Propermorphism, in algebraic geometry, an analogue of a proper map for algebraic varieties Proper transfer function, a transfer...
a propermorphism. Then one can write f = g ∘ f ′ {\displaystyle f=g\circ f'} where g : S ′ → S {\displaystyle g\colon S'\to S} is a finite morphism and...
a scheme will be a scheme over some fixed base scheme S and a morphism an S-morphism. Contents: !$@ A B C D E F G H I J K L M N O P Q R S T U V W XYZ...
of positive dimension is not complete. The morphism taking a complete variety to a point is a propermorphism, in the sense of scheme theory. An intuitive...
} Proper base change theorems for quasi-coherent sheaves apply in the following situation: f : X → S {\displaystyle f:X\to S} is a propermorphism between...
of Jean-Pierre Serre was extended to a propermorphism; Serre duality was recovered as the case of the morphism of a non-singular projective variety (or...
theory of schemes in algebraic geometry, a flat morphism f from a scheme X to a scheme Y is a morphism such that the induced map on every stalk is a flat...
finite surjective morphism f: X → Y, X and Y have the same dimension. By Deligne, a morphism of schemes is finite if and only if it is proper and quasi-finite...
bundle L. This morphism has the property that L is the pullback f ∗ O ( 1 ) {\displaystyle f^{*}O(1)} . Conversely, for any morphism f from a scheme...
a propermorphism were proved by Grothendieck (for locally Noetherian schemes) and by Grauert (for complex analytic spaces). Namely, for a proper morphism...
respectively. The morphism f is determined by its values on the letters of B and conversely any map from B to M extends to a morphism. A morphism is non-erasing...
of sheaves, and states that ch(f*(E))= f*(ch(E)TdX/Y), where f is a propermorphism from X to Y and E is a vector bundle over f. The arithmetic Riemann–Roch...
surface is a surface that has an elliptic fibration, in other words a propermorphism with connected fibers to an algebraic curve such that almost all fibers...
Morph the Cat is the third studio album by American singer-songwriter Donald Fagen. Released on March 7, 2006, to generally positive reviews from critics...
Parafactorial local ring Projective tensor product Propermorphism – in algebraic geometry, an analogue of a proper map for algebraic varietiesPages displaying...
morphism of schemes generalizes a morphism of algebraic varieties just as a scheme generalizes an algebraic variety. It is, by definition, a morphism...
G-maps. The composition of two morphisms is again a morphism. If a morphism f is bijective, then its inverse is also a morphism. In this case f is called an...
associated to the propermorphism Z → X {\displaystyle Z\to X} , and the second homomorphism is pullback with respect to the flat morphism X − Z → X {\displaystyle...
a universal morphism from • to U. The functor which sends • to I is left adjoint to U. A terminal object T in C is a universal morphism from U to •....
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